Assume a binomial model for a certain random variable. If we desire a 90% confidence interval...

Question

Question

Assume a binomial model for a certain random variable. If we desire a 90% confidence interval for p that is at most 0.02 in length, find n.

Hint: Note that (sqrt (y/n)*(1 − y/n)) ≤ (sqrt( 1/2 )*(1 − 1 /2 ))

math Statistics-And-Probability

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

4.2.16. Assume a binomial model for a certain randon variable. If we desire a 90% confidence...

4.2.16. Assume a binomial model for a certain randon variable. If we desire a 90% confidence interval for p that is at most 0.02 in length, find n. lHint: Note that um-ym)s ya-
(2) Let Y be a binomial random variable with parameters n and p. Remember that We...

(2) Let Y be a binomial random variable with parameters n and p. Remember that We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n借)(1-n) (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random...

Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where tan (∙) denotes the tangent function. Note that the derivative of tan (?) is 1/(cos (?)2) . a) Find the PDF of ?. b) Find the mean of ? .Define the random variable ?=1/?. c) Find the PDF of ?. Assume random variable X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...

Suppose X is a Binomial Random Variable with n = 4 and p = 2. What...

Suppose X is a Binomial Random Variable with n = 4 and p = 2. What is the pdf of Y = 2X + 1? Note: The pdf of a Binomial Random Variable X is pX(k) = n k (1 − p) kp n−k , k = 0, 1, 2, . . . ,
2. Assume the random variable y has the continuous uniform distribution defined on the interval a...

2. Assume the random variable y has the continuous uniform distribution defined on the interval a to b, that is, f(y) = 1/6 - a), a sy<b. For this problem let a = 0 and b = 2. (a) Find P(Y < 1). (Hint: Use a picture.) (b) Find u and o2 for the distribution.
(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y)...

(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) V(Y)p1 -p) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(2(1 (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator

Let N be a binomial random variable with p = 0.2 and n = 10. We...

Let N be a binomial random variable with p = 0.2 and n = 10. We roll a fair die N times, let X be the number of times we roll the number 1. Find the joint probability mass function of N and X.
Recall the formula for a proportion confidence interval is p^?zp^(1?p^)n?????????<p<p^+zp^(1?p^)n????????? Thus, the margin of error is...

Recall the formula for a proportion confidence interval is p^?zp^(1?p^)n?????????<p<p^+zp^(1?p^)n????????? Thus, the margin of error is E=zp^(1?p^)n????????? . NOTE: the margin of error can be recovered after constructing a confidence interval on the calculator using algebra (that is, subtracting p^ from the right endpoint.) In a simple random sample of size 59, taken from a population, 20 of the individuals met a specified criteria. a) What is the margin of error for a 90% confidence interval for p, the population...
2) we want to develop a 90% confidence interval for the fraction of fruit flies which...

2) we want to develop a 90% confidence interval for the fraction of fruit flies which possess a gene for red eyes. To this end we obtain a simple random sample of 200 fruit flies, we find that 35% of the flies in the sample possess the gene. Give a 90% confidence interval for the fraction of all fruit flies with the gene a) 0.29 to 0.41 b) 0.28 to 0.42 c) 0.26 to 0.44 d) 0.31 to 0.39 e)...

Assume the random variable x has a binomial distribution with a given probability of obtaining a...

Assume the random variable x has a binomial distribution with a given probability of obtaining a success. Find the probability, given the number of trials and the probability of obtaining a success. P(X<=3), n=7, p=.2